{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Generative model for the Olympic 100m</h2>\n",
    "<p>We will now look at generating data that looks a bit like the Olympic 100m data. We'll start by getting the data.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import urllib\n",
    "# urllib.urlretrieve('https://github.com/sdrogers/fcml/raw/master/notebooks/data/olympic100m.txt', 'olympic100m.txt')\n",
    "import numpy as np\n",
    "data = np.loadtxt('olympic100m.txt',delimiter=',')\n",
    "x = data[:,0][:,None]\n",
    "t = data[:,1][:,None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We'll assume that we know the true parameter values and look at generating the noise. We'll get the true parameter values by minimising the loss...</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  3.64164559e+01]\n",
      " [ -1.33308857e-02]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "X = np.hstack((np.ones_like(x),x))\n",
    "w = np.dot(np.linalg.inv(np.dot(X.T,X)),np.dot(X.T,t))\n",
    "print w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Choose values for the mean and variance of the noise</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mu = 0.0\n",
    "sigma_sq = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Generate the noisy t values (note that `numpy.random.normal` requires the standard deviation, not the variance)</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "noisy_t = np.dot(X,w) + np.random.normal(mu,np.sqrt(sigma_sq),(t.size,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Plot the noisy data</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1117d17d0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kOOggWHHF/gUakWyjoBEHBQ2R9IhEIjQ1NXW7PxwO09jYmLoG9VFrq7+6MX06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\nk31akJzOvm8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1117d16d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab as plt\n",
    "%matplotlib inline\n",
    "plt.plot(x,noisy_t,'ko')\n",
    "plt.plot(x,np.dot(X,w),'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>A second plot, this time with the real data included</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x111755950>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wOExVVRWNjY05bfbfZx//uvpq38pxww3w85/7FOfnnAMnn+xHteTKSDK4FlpL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\nKHMGwiE7T9jUlroAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116a4610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab as plt\n",
    "%matplotlib inline\n",
    "plt.plot(x,noisy_t,'ko')\n",
    "plt.plot(x,np.dot(X,w),'b')\n",
    "plt.plot(x,t,'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
